On the linear twist of degree 1 functions in the extended Selberg class

Giamila Zaghloul

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arXiv · 1903.06145

On the linear twist of degree 1 functions in the extended Selberg class

Giamila Zaghloul

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Abstract

Given a degree 1 function $F\in\mathcal{S}^{\sharp}$ and a real number $\alpha$, we consider the linear twist $F(s,\alpha)$, proving that it satisfies a functional equation reflecting $s$ into $1-s$, which can be seen as a Hurwitz-Lerch type of functional equation. We also derive some results on the distribution of the zeros of the linear twist.

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Giamila Zaghloul. 2019-03-14. On the linear twist of degree 1 functions in the extended Selberg class. https://arxiv.org/abs/1903.06145

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